Iran
The ever-deepening rift between Iran and the U.S. began back in 1979 with the Iranian Revolution and the Iran hostage crisis; the country has had no formal diplomatic relations with America since 1980. A BBC poll conducted in 2013 found that only 13% of Iranians have a favorable view of the United States, making it the country with the least favorable perception of America in the entire world.
Russia
Russia and the U.S. are two of the most powerful nations in the world, and they are on famously prickly terms. What was once a warm relationship began to deteriorate in 1999 after the NATO bombing of the Federal Republic of Yugoslavia; things only escalated during the past few decades' presidential elections. These days, according to a Pew survey, 71% of Russians have an unfavorable perception of Americans.